The 4th term of a G.P.is square of its second term and the first term

1.	The 4th term of a G.P.is square of its second term and the first term is – 3. Determine its 7th term.
Answer» Let G.P.be a, ar, ar² ,………….. , then T_n = ar^{n - 1} Given: a = - 3 and T₄ = (T₂)² since T₄ = (T₂)²then ar³ = (ar)² ⇒ (-3)r₃ = (-3r)² = 9r² ⇒ r³/r² = 9/-3 ⇒ r = - 3 Hence, 7^th term = ar⁶ = (-3)(-3)⁶ = (-3)⁷ = - 2187 The first term, a of the G.P. is given as –3. The nth term of the G.P. is given by a_n = ar^n-1 ∴Second term, a₂ = ar = –3r 4th term, a₄ = ar³ = –3r³ It is given that, –3r³= (–3r)² . ∴ –3r³ = 9r² ⇒ r = –3 Thus, 7th term, a₇ = ar6 = –3*(–3)⁶ = –2187

The 4th term of a G.P.is square of its second term and the first term is – 3. Determine its 7th term.

Answer»

Let G.P.be a, ar, ar² ,………….. , then

T_n = ar^{n - 1}

Given: a = - 3 and T₄ = (T₂)²

since T₄ = (T₂)²then

ar³ = (ar)²

⇒ (-3)r₃ = (-3r)² = 9r²

⇒ r³/r² = 9/-3 ⇒ r = - 3

Hence, 7^th term = ar⁶ = (-3)(-3)⁶

= (-3)⁷ = - 2187

The first term, a of the G.P. is given as –3.

The nth term of the G.P. is given by a_n = ar^n-1

∴Second term, a₂ = ar = –3r

4th term, a₄ = ar³ = –3r³

It is given that, –3r³= (–3r)² .

∴ –3r³ = 9r² ⇒ r = –3

Thus, 7th term, a₇ = ar6 = –3*(–3)⁶ = –2187